Problem: Ben is 40 years older than Omar. For the last four years, Ben and Omar have been going to the same school. Eleven years ago, Ben was 5 times older than Omar. How old is Ben now?
Answer: We can use the given information to write down two equations that describe the ages of Ben and Omar. Let Ben's current age be $b$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $b = o + 40$ Eleven years ago, Ben was $b - 11$ years old, and Omar was $o - 11$ years old. The information in the second sentence can be expressed in the following equation: $b - 11 = 5(o - 11)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = b - 40$ . Substituting this into our second equation, we get the equation: $b - 11 = 5($ $(b - 40)$ $ -$ $ 11)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 11 = 5b - 255$ Solving for $b$ , we get: $4 b = 244$ $b = 61$.